We study the problem of maintaining a dynamic ordered set subject to
insertions, deletions, and traversals of k consecutive elements. This
problem is trivially solved on a RAM and on a simple two-level memory
hierarchy. We explore this traversal problem on more realistic memory models:
the cache-oblivious model, which applies to unknown and multi-level memory
hierarchies, and sequential-access models, where sequential block transfers are
less expensive than random block transfers.